Question: Tiffany is 2 years older than Emily. Two years ago, Tiffany was 3 times as old as Emily. How old is Emily now?
Explanation: We can use the given information to write down two equations that describe the ages of Tiffany and Emily. Let Tiffany's current age be $t$ and Emily's current age be $e$ The information in the first sentence can be expressed in the following equation: $t = e + 2$ Two years ago, Tiffany was $t - 2$ years old, and Emily was $e - 2$ years old. The information in the second sentence can be expressed in the following equation: $t - 2 = 3(e - 2)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $e$ , it might be easiest to use our first equation for $t$ and substitute it into our second equation. Our first equation is: $t = e + 2$ . Substituting this into our second equation, we get the equation: $(e + 2)$ $-$ $2 = 3(e - 2)$ which combines the information about $e$ from both of our original equations. Simplifying both sides of this equation, we get: $e + 0 = 3 e - 6$ Solving for $e$ , we get: $2 e = 6$ $e = 3$.